{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_data.shape: (118, 2)\n",
      "y_data.shape: (118,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as op\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "data = np.loadtxt('..\\data_sets\\ex2data2.txt', delimiter = ',')\n",
    "x_data = data[:, 0:2]\n",
    "y_data = data[:, 2]\n",
    "print('x_data.shape:', x_data.shape)\n",
    "print('y_data.shape:', y_data.shape)\n",
    "\n",
    "def plotdata(data):\n",
    "    positive = data[data[:, 2] == 1]\n",
    "    negative = data[data[:, 2] == 0]\n",
    "    plt.xlabel('Test_1')\n",
    "    plt.ylabel('Test_2')\n",
    "    plt.scatter(positive[:, 0], positive[:, 1], c = 'r', marker = 'o', label = 'Accepted')\n",
    "    plt.scatter(negative[:, 0], negative[:, 1], c = 'black', marker = 'x', label = 'Rejected')\n",
    "    plt.legend(loc = 3)\n",
    "    \n",
    "plt.figure(0)    \n",
    "plotdata(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Feature mapping\n",
    "def feature_map(x1, x2, power):\n",
    "    x0 = np.ones(x1.size)\n",
    "    result = x0\n",
    "    for i in range(1, power + 1):\n",
    "        for j in range(i + 1):\n",
    "            x_ = x1**(i-j)*x2**j\n",
    "#     for i in range(power + 1):\n",
    "#         for j in range(power + 1 - i):\n",
    "#             if i == 0 and j == 0:\n",
    "#                 continue\n",
    "#             x_ = x1**i*x2**j\n",
    "            result = np.column_stack((result, x_))\n",
    "    return result\n",
    "\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))\n",
    "\n",
    "def cost_function(theta, x, y, L = 0):\n",
    "    m = y.size\n",
    "    theta_ = theta[1:]\n",
    "    return (-1 / m) * (y @ np.log(sigmoid(x @ theta)) + (1 - y) @ np.log(1 - sigmoid(x @ theta))) + L / (2*m) * np.sum(theta_**2)\n",
    "\n",
    "def gradient(theta, x, y, L = 0):\n",
    "    m = y.size\n",
    "    theta_ = (L / m) * theta \n",
    "    theta_[0] = 0\n",
    "    return (1 / m) * ((sigmoid(x @ theta) - y) @ x) + theta_\n",
    "\n",
    "def plot_boundary(theta):\n",
    "    u = np.linspace(-1, 1.2, 50)\n",
    "    v = np.linspace(-1, 1.2, 50)\n",
    "    z = np.zeros((u.size, v.size)) #  it can also use z = np.meshgrid(u, v)\n",
    "    for i in range(u.size):\n",
    "        for j in range(v.size):\n",
    "            x_ = feature_map(u[i], v[j], 6)\n",
    "            z[i][j] = x_ @ theta\n",
    "    C = plt.contour(u, v, z, 0, colors = 'b')\n",
    "    plt.clabel(C,inline=True,fontsize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_data.shape: (118, 28)\n",
      "y_data.shape: (118,)\n",
      "theta.shape: (28,)\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.266508\n",
      "         Iterations: 2386\n",
      "         Function evaluations: 8863\n",
      "         Gradient evaluations: 8863\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.529003\n",
      "         Iterations: 19\n",
      "         Function evaluations: 55\n",
      "         Gradient evaluations: 55\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.686484\n",
      "         Iterations: 7\n",
      "         Function evaluations: 11\n",
      "         Gradient evaluations: 11\n",
      "(28,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# build the model\n",
    "x_data = feature_map(x_data[:, 0], x_data[:, 1], 6)\n",
    "print('x_data.shape:', x_data.shape)\n",
    "print('y_data.shape:', y_data.shape)\n",
    "theta = np.zeros(x_data[0].size)\n",
    "print('theta.shape:', theta.shape)\n",
    "\n",
    "# plot decision boundary\n",
    "lambda_ = 0\n",
    "result_CG = op.minimize(fun = cost_function, x0 = theta, args = (x_data, y_data, lambda_), method = 'CG', jac = gradient, options={\"disp\":True})\n",
    "plt.figure(1)\n",
    "plotdata(data)\n",
    "plot_boundary(result_CG['x'])\n",
    "plt.title('Lambda = 0')\n",
    "\n",
    "lambda_ = 1\n",
    "result_CG = op.minimize(fun = cost_function, x0 = theta, args = (x_data, y_data, lambda_), method = 'CG', jac = gradient, options={\"maxiter\":500, \"disp\":True})\n",
    "plt.figure(2)\n",
    "plotdata(data)\n",
    "plot_boundary(result_CG['x'])\n",
    "plt.title('Lambda = 1')\n",
    "\n",
    "lambda_ = 100\n",
    "result_CG = op.minimize(fun = cost_function, x0 = theta, args = (x_data, y_data, lambda_), method = 'CG', jac = gradient, options={\"maxiter\":500, \"disp\":True})\n",
    "plt.figure(3)\n",
    "plotdata(data)\n",
    "plot_boundary(result_CG['x'])\n",
    "plt.title('Lambda = 100')\n",
    "\n",
    "print(result_CG['x'].shape)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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